A nodal integration and post-processing technique based on Voronoi diagram for Galerkin meshless methods

A stabilized nodal integration technique is adopted by adding the square of the residual of the equilibrium equation to the potential energy functional. An approach is proposed based on Voronoi diagram to evaluate nodal volumes accurately. It is a key issue for nodal integration of Galerkin meshless methods. Furthermore, as the dual of Voronoi diagram, the corresponding Delaunay triangles are at hand provided Voronoi diagram construction is completed. A realistic technique is proposed based on background Delaunay triangles for post-processing of meshless results in the whole domain of interest. Two elastic stress analysis problems are investigated, which demonstrate the approach is realistic, versatile and robust.